Question 1

Rationalize the denominator. Assume that all variables represent positive real numbers. 
-$\sqrt{\frac{100}{3}}$

Accepted Answer

A)  $10 \sqrt{3}$ 
B)  19 
C)  $\frac{100 \sqrt{3}}{3}$ 
D)  $\frac{10 \sqrt{3}}{3}$ 
A)  $10 \sqrt{3}$ 
B)  19 
C)  $\frac{100 \sqrt{3}}{3}$ 
D)  $\frac{10 \sqrt{3}}{3}$

Question 2

The radius of a sphere is given by the formula $r=\sqrt{\frac{S}{4 \pi}}$, where $S$ is the surface area. If the surface area is 8709 square inches, what is the radius? Use 3.14 for $\pi$, and round your answer to the nearest tenth of an inch.

Accepted Answer

A)  46.7 inches 
B)  82.7 inches 
C)  0 inches 
D)  26.3 inches 
A)  46.7 inches 
B)  82.7 inches 
C)  0 inches 
D)  26.3 inches

Question 3

Simplify the expression involving rational exponents.
-$\left(\frac{16}{49}\right)^{-1 / 2}$

Accepted Answer

A)  $\frac{8}{49}$ 
B)  $\frac{4}{7}$ 
C)  Not a real number 
D)  $\frac{7}{4}$ 
A)  $\frac{8}{49}$ 
B)  $\frac{4}{7}$ 
C)  Not a real number 
D)  $\frac{7}{4}$

Question 4

Choose the one alternative that best completes the statement or answers the question.
Multiply using the product rule.
-$\sqrt[3]{9 x y} \cdot \sqrt[3]{25 x y}$

Accepted Answer

A)  $\sqrt[3]{225 x^{2} y^{2}}$ 
B)  $\sqrt[3]{34 x^{2} y^{2}}$ 
C)  $8 x y$ 
D)  $15 x y$ 
A)  $\sqrt[3]{225 x^{2} y^{2}}$ 
B)  $\sqrt[3]{34 x^{2} y^{2}}$ 
C)  $8 x y$ 
D)  $15 x y$

Question 5

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$\frac{y^{9 / 8}}{y^{5 / 8}}$

Accepted Answer

A)  $y^{1 / 2}$ 
B)  $\frac{1}{y}$ 
C)  $y$ 
D)  $y^{9 / 8}$ 
A)  $y^{1 / 2}$ 
B)  $\frac{1}{y}$ 
C)  $y$ 
D)  $y^{9 / 8}$

Question 6

Multiply, then simplify the product. Assume that all variables represent positive real numbers.
-$(2-2 \sqrt{2})^{2}$

Accepted Answer

A)  $12-8 \sqrt{2}$ 
B)  $4+4 \sqrt{2}$ 
C)  $4-4 \sqrt{2}$ 
D)  $12+8 \sqrt{2}$ 
A)  $12-8 \sqrt{2}$ 
B)  $4+4 \sqrt{2}$ 
C)  $4-4 \sqrt{2}$ 
D)  $12+8 \sqrt{2}$

Question 7

Simplify the expression involving rational exponents.
-$81^{5 / 4}$

Accepted Answer

A)  243 
B)  2187 
C)  6561 
D)  19,683 
A)  243 
B)  2187 
C)  6561 
D)  19,683

Question 8

Simplify. Assume that all variables represent positive real numbers.
-$\frac{-3}{\sqrt{15}}$

Accepted Answer

A)  $-\frac{\sqrt{15}}{5}$ 
B)  $\frac{\sqrt{15}}{5}$ 
C)  -3 
D)  $-\sqrt{3}$ 
A)  $-\frac{\sqrt{15}}{5}$ 
B)  $\frac{\sqrt{15}}{5}$ 
C)  -3 
D)  $-\sqrt{3}$

Question 9

Write the expression in the form a + bi.
-$\frac{1-7 i}{5-3 i}$

Accepted Answer

A)  $\frac{14}{17}-\frac{15}{17} \mathrm{i}$ 
B)  $\frac{15}{17}-\frac{14}{17} \mathrm{i}$ 
C)  $\frac{13}{17}-\frac{16}{17} \mathrm{i}$ 
D)  $\frac{16}{17}-\frac{13}{17} \mathrm{i}$ 
A)  $\frac{14}{17}-\frac{15}{17} \mathrm{i}$ 
B)  $\frac{15}{17}-\frac{14}{17} \mathrm{i}$ 
C)  $\frac{13}{17}-\frac{16}{17} \mathrm{i}$ 
D)  $\frac{16}{17}-\frac{13}{17} \mathrm{i}$

Question 10

Find the distance between the pair of points.
-$(7,-1)$ and $(5,-5)$

Accepted Answer

A)  2 
B)  $2 \sqrt{5}$ 
C)  $12 \sqrt{3}$ 
D)  12 
A)  2 
B)  $2 \sqrt{5}$ 
C)  $12 \sqrt{3}$ 
D)  12

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{8 q-7}=7$

Accepted Answer

A)  $\left\{\frac{21}{4}\right\}$ 
B)  $\{49\}$ 
C)  $\left\{\frac{49}{8}\right\}$ 
D)  $\{7\}$ 
A)  $\left\{\frac{21}{4}\right\}$ 
B)  $\{49\}$ 
C)  $\left\{\frac{49}{8}\right\}$ 
D)  $\{7\}$

Question 12

Tell whether the statement is true or false. If it is false, give the correct answer. Explain.
$\sqrt[4]{x} \cdot \sqrt[4]{x}=x$

Accepted Answer

A) True 
 B)False

Question 13

Add or subtract as indicated. Write your answer in the form $a+b i$.
-$(5-4 \mathrm{i})+(9+6 \mathrm{i})$

Accepted Answer

A)  $14-2 \mathrm{i}$ 
B)  $-14-2 \mathrm{i}$ 
C)  $14+2 i$ 
D)  $-4+10 \mathrm{i}$ 
A)  $14-2 \mathrm{i}$ 
B)  $-14-2 \mathrm{i}$ 
C)  $14+2 i$ 
D)  $-4+10 \mathrm{i}$

Question 14

Find the unknown length in the right triangle. Simplify the answer if necessary.
-

Accepted Answer

A)  $2 \sqrt{15}$ 
B)  $\sqrt{10}$ 
C)  $2 \sqrt{17}$ 
D)  $\sqrt{6}$ 
A)  $2 \sqrt{15}$ 
B)  $\sqrt{10}$ 
C)  $2 \sqrt{17}$ 
D)  $\sqrt{6}$

Question 15

Simplify the expression involving rational exponents.
-$-\left(\frac{25}{49}\right)^{1 / 2}$

Accepted Answer

A)  Not a real number 
B)  $-\frac{25}{98}$ 
C)  $-\frac{5}{7}$ 
D)  $\frac{7}{5}$ 
A)  Not a real number 
B)  $-\frac{25}{98}$ 
C)  $-\frac{5}{7}$ 
D)  $\frac{7}{5}$

Question 16

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}$

Accepted Answer

A)  $\left(2 x^{3} y^{2}-3 x^{4} y\right) \sqrt[3]{4 y}$ 
B)  $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4 y}$ 
C)  $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4}$ 
D)  $\left(2 x^{6} y^{4}-3 x^{9} y\right) \sqrt[3]{4}$ 
A)  $\left(2 x^{3} y^{2}-3 x^{4} y\right) \sqrt[3]{4 y}$ 
B)  $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4 y}$ 
C)  $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4}$ 
D)  $\left(2 x^{6} y^{4}-3 x^{9} y\right) \sqrt[3]{4}$

Question 17

Write the number as a product of a real number and $i$. Simplify the radical expression.
-$\sqrt{-49}$

Accepted Answer

A)  $i \sqrt{7}$ 
B)  $7 \mathrm{i}$ 
C)  $-7 \mathrm{i}$ 
D)  ± 7 
A)  $i \sqrt{7}$ 
B)  $7 \mathrm{i}$ 
C)  $-7 \mathrm{i}$ 
D)  ± 7

Question 18

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
-$\sqrt[4]{9 x^{6}}$

Accepted Answer

A)  $\sqrt[x]{3 x^{2}}$ 
B)  $3 x^{3}$ 
C)  $\sqrt[4]{9 x^{6}}$ 
D)  $\sqrt{3 x^{3}}$ 
A)  $\sqrt[x]{3 x^{2}}$ 
B)  $3 x^{3}$ 
C)  $\sqrt[4]{9 x^{6}}$ 
D)  $\sqrt{3 x^{3}}$

Question 19

Simplify the root.
-$\sqrt[6]{(-2)^{6}}$

Accepted Answer

A)  -2 
B)  4 
C)  Not a real number 
D)  2 
A)  -2 
B)  4 
C)  Not a real number 
D)  2

Question 20

Is $\sqrt{16}=4$ ?

Accepted Answer

A) True 
 B)False

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\sqrt{\frac{100}{3}}$

The radius of a sphere is given by the formula $r=\sqrt{\frac{S}{4 \pi}}$ , where $S$ is the surface area. If the surface area is 8709 square inches, what is the radius? Use 3.14 for $\pi$ , and round your answer to the nearest tenth of an inch.

Simplify the expression involving rational exponents. - $\left(\frac{16}{49}\right)^{-1 / 2}$

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - $\sqrt[3]{9 x y} \cdot \sqrt[3]{25 x y}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\frac{y^{9 / 8}}{y^{5 / 8}}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(2-2 \sqrt{2})^{2}$

Simplify the expression involving rational exponents. - $81^{5 / 4}$

Simplify. Assume that all variables represent positive real numbers. - $\frac{-3}{\sqrt{15}}$

Write the expression in the form a + bi. - $\frac{1-7 i}{5-3 i}$

Find the distance between the pair of points. - $(7,-1)$ and $(5,-5)$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{8 q-7}=7$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain. $\sqrt[4]{x} \cdot \sqrt[4]{x}=x$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(5-4 \mathrm{i})+(9+6 \mathrm{i})$

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Simplify the expression involving rational exponents. - $-\left(\frac{25}{49}\right)^{1 / 2}$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-49}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[4]{9 x^{6}}$

Simplify the root. - $\sqrt[6]{(-2)^{6}}$

Is $\sqrt{16}=4$ ?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 8: Roots, Radicals, and Root Functions

Rationalize the denominator. Assume that all variables represent positive real numbers. - 1003\sqrt{\frac{100}{3}}3100​​

The radius of a sphere is given by the formula r=S4πr=\sqrt{\frac{S}{4 \pi}}r=4πS​​ , where SSS is the surface area. If the surface area is 8709 square inches, what is the radius? Use 3.14 for π\piπ , and round your answer to the nearest tenth of an inch.

Simplify the expression involving rational exponents. - (1649)−1/2\left(\frac{16}{49}\right)^{-1 / 2}(4916​)−1/2

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - 9xy3⋅25xy3\sqrt[3]{9 x y} \cdot \sqrt[3]{25 x y}39xy​⋅325xy​

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - y9/8y5/8\frac{y^{9 / 8}}{y^{5 / 8}}y5/8y9/8​

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - (2−22)2(2-2 \sqrt{2})^{2}(2−22​)2

Simplify the expression involving rational exponents. - 815/481^{5 / 4}815/4

Simplify. Assume that all variables represent positive real numbers. - −315\frac{-3}{\sqrt{15}}15​−3​

Write the expression in the form a + bi. - 1−7i5−3i\frac{1-7 i}{5-3 i}5−3i1−7i​

Find the distance between the pair of points. - (7,−1)(7,-1)(7,−1) and (5,−5)(5,-5)(5,−5)

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 8q−7=7\sqrt{8 q-7}=78q−7​=7

Tell whether the statement is true or false. If it is false, give the correct answer. Explain. x4⋅x4=x\sqrt[4]{x} \cdot \sqrt[4]{x}=x4x​⋅4x​=x

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - (5−4i)+(9+6i)(5-4 \mathrm{i})+(9+6 \mathrm{i})(5−4i)+(9+6i)

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Simplify the expression involving rational exponents. - −(2549)1/2-\left(\frac{25}{49}\right)^{1 / 2}−(4925​)1/2

Simplify. Assume that all variables represent positive real numbers. - 32x9y73−108x12y43\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}332x9y7​−3108x12y4​

Write the number as a product of a real number and iii . Simplify the radical expression. - −49\sqrt{-49}−49​

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - 9x64\sqrt[4]{9 x^{6}}49x6​

Simplify the root. - (−2)66\sqrt[6]{(-2)^{6}}6(−2)6​

Is 16=4\sqrt{16}=416​=4 ?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\sqrt{\frac{100}{3}}$

The radius of a sphere is given by the formula $r=\sqrt{\frac{S}{4 \pi}}$ , where $S$ is the surface area. If the surface area is 8709 square inches, what is the radius? Use 3.14 for $\pi$ , and round your answer to the nearest tenth of an inch.

Simplify the expression involving rational exponents. - $\left(\frac{16}{49}\right)^{-1 / 2}$

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - $\sqrt[3]{9 x y} \cdot \sqrt[3]{25 x y}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\frac{y^{9 / 8}}{y^{5 / 8}}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(2-2 \sqrt{2})^{2}$

Simplify the expression involving rational exponents. - $81^{5 / 4}$

Simplify. Assume that all variables represent positive real numbers. - $\frac{-3}{\sqrt{15}}$

Write the expression in the form a + bi. - $\frac{1-7 i}{5-3 i}$

Find the distance between the pair of points. - $(7,-1)$ and $(5,-5)$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{8 q-7}=7$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain. $\sqrt[4]{x} \cdot \sqrt[4]{x}=x$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(5-4 \mathrm{i})+(9+6 \mathrm{i})$

Simplify the expression involving rational exponents. - $-\left(\frac{25}{49}\right)^{1 / 2}$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-49}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[4]{9 x^{6}}$

Simplify the root. - $\sqrt[6]{(-2)^{6}}$

Is $\sqrt{16}=4$ ?